GRACEFUL CHROMATIC NUMBER OF THE FAMILY OF CENTRIPETAL GRAPH

Abstract

One of the topics studied in graphs is graph coloring. The definition of a graceful coloring, namely $k$-elegant coloring of a graph G is the exact vertex coloring c:V(G)→{ 1,2,...,k} where k≥2 induces the exact vertex coloring c^': V(G)→ {1,2,...,k-1} which is defined by c(uv)=|c(u)-c(v)|. The exact vertex coloring c of a graph G is a graceful coloring if c is a k-elegant coloring for k∈N. The graceful chromatic number is the minimum k value where graph G has k-elegant coloring, the elegant chromatic number of graph G is denoted by X_g (G). This article will discuss graceful chromatic numbers in the centripetal graph family which includes octopus graph (O_n), sandat graph (St_n),dutch windmill graph (D_3^m) , and a volcano graph (V_n).